Question

Jane sells boxes of cookies for $8 each. Sam sells boxes of cookies for $10 each. Each of them sold the same dollar amount. It was the smallest dollar amount for which this was possible.

Answer 1

In order to solve this problem, we need to find the least common multiple of 8 and 10. The first step to doing this is finding the prime factorization of 8 and 10.

8 is 2*2*2, and 10 is 2*5. The two factors of 8 and 10 are 2 and 5. Now, we multiply 2 by the greatest amount of times it occurs. This is 3, coming from the prime factorization of 8. Next, we multiply 5 by the greatest amount of times it occurs. This is simply 1, because it only pops up once.

This is: 2*2*2*5 = 40, so 40 is the least common multiple. Because the least common multiple of 8 and 10, $40 is the smallest dollar amount that Jane and Sam could have made.